Spacecraft—artificial satellites or probes—are generally injected by a launch vehicle into a so-called injection earth orbit, which does not correspond to the orbit, not necessarily an earth orbit, that it has to reach to accomplish its mission (“stationing”), for example a geostationary orbit for a telecommunications satellite. Moreover, the missions of space exploration probes generally comprise several phases characterized by different orbits. It is therefore essential to be able to accurately perform orbit transfer manoeuvres.
In the case of “conventional” spacecraft with chemical propulsion, the orbit transfer is performed using thrusts that are very intense and very short relative to an orbit period. Typically, a first thrust ejects the spacecraft from its initial orbit (for example, injection orbit) and positions it on a so-called transfer orbit, which is chosen in such a way as to cross the target, or destination, orbit. When the spacecraft has arrived close to the crossing point, a second thrust places it on said target orbit.
Electric propulsion systems are experiencing significant development because they make it possible to very greatly limit the weight of propellant necessary to impart a given impulse on the spacecraft. That makes it possible to reduce the weight of the craft at launch and/or prolong its life. Electric propulsion provides a thrust that is weaker by several orders of magnitude compared to chemical thrust, but it can be maintained, uninterrupted or intermittently over durations that are comparable (for example, not less than a tenth) to the orbit transfer duration; in this case continuous or “quasi-continuous” thrust applies. The orbit transfer is therefore performed in a very different way to the case of chemical propulsion—by a progressive deformation of the starting orbit. By way of example, FIG. 1 illustrates the gradual transfer from an initial elliptical orbit OI to a circular target orbit OC.
There therefore arises the problem of controlling the intensity and the orientation of the thrust throughout the transfer phase.
Conventionally, the control is performed in open-loop mode: an optimal control law is computed on the ground and transmitted to the on-board computer which drives the propulsion system. At regular intervals, for example once a week, a new control law is recomputed taking into account the real position and velocity of the spacecraft, which generally will not exactly correspond to those expected. Such an approach is cumbersome to implement, because the trajectory optimization computations are very complex (they involve solving a problem of nonlinear optimization under constraints that are also nonlinear). Moreover, between two successive updates of the control law, the spacecraft can deviate significantly from its ideal trajectory which increases the duration of the transfer phase and the consumption of propellant.
The article by Thierry Dargent “Averaging technique in T-3D: an integrated tool for continuous thrust optimal control in orbit transfers,” AAS 14-312 (2014) describes a technique for computing a continuous or quasi-continuous thrust optimal control law that can be used in an open-loop approach.
It is also known practice to use so-called stabilization heuristics type techniques, which are based—implicitly—on the minimization of a control-Lyapunov function. A technique of this type, called “Q-Law”, used mainly as pre-dimensioning method, is described in the following articles:
A. E. Petropoulos, S. Lee “Optimisation of low-thrust orbit transfers using the Q-Law for the initial guess”, AAS/AIAA Astrodynamics Specialists Conference, 2005;
S. Lee et al. “Design and Optimization of Low-thrust Orbit Transfer” in: Aerospace Conference, 2005 IEEE. IEEE, 2005. p. 855-869;
A. E. Petropoulos et al. “Techniques for designing many-revolution, electric-propulsion trajectories”, AAS 14-373, 2014.
This technique does not give total satisfaction. On the one hand, it presents problems of instability, notably in the case of orbits with low eccentricity and low inclination, which are of very significant practical interest (simply consider the geostationary orbits, which have a zero eccentricity and inclination), and on the other hand it leads to results that are quite far removed from an optimal control law, unless there is recourse to sophisticated techniques (optimization of weighting coefficients using genetic algorithms). Moreover, it does not make it possible to manage the longitude encounter constraints which are very significant in the case of the stationing of geostationary satellites.
To remedy the drawbacks of the open-loop control, it would be desirable to adopt a closed-loop (feedback loop) approach, in which an embedded processor computes in real time the control to be applied to the propulsion system by taking into account the position and velocity of the spacecraft, determined for example using a satellite navigation system (GNSS, “Global Navigation Satellite System”). Since the computation power of the embedded processors is limited, it does however appear difficult to implement an optimal control law in closed-loop mode.
The invention aims to overcome the abovementioned drawbacks of the prior art, and more particularly to obtain a technique for closed-loop control of the continuous or quasi-continuous thrust to perform an orbit transfer which is at the same time stable, simple to implement and close to optimal. Advantageously, such a technique can make it possible to manage the longitude encounter constraints.
According to the invention, this aim is achieved by virtue of the use of a heuristic control law which, as in the case of the Q-Law, is obtained from a Control-Lyapunov function but which:
expresses this function by means of equinoctial orbital parameters, instead of the “conventional” orbital parameters used in the prior art; and
uses (equinoctial) orbital parameters averaged over at least one half-period of revolution.